Worksheets — Set 13

Probability · Common distributions and limit theorems

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. P(A) = 1, P(B) = 1.1. If independent, P(A∩B) = ___ 2. Binomial(n=19, p=0.5): P(X = 16) = ___ 3. E[X] for X with values {15, 17, 19} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 0.95, P(B) = 1.05. If independent, P(A∩B) = ___ 2. Binomial(n=18, p=0.5): P(X = 15) = ___ 3. E[X] for X with values {14, 16, 18} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.36 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.1, P(B) = 1.2000000000000002. If independent, P(A∩B) = ___ 8. Binomial(n=21, p=0.5): P(X = 18) = ___

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More written practice

1. E[X] for X with values {17, 19, 21} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.42000000000000004 ___ 3. P(A) = 1.25, P(B) = 1.35. If independent, P(A∩B) = ___ 4. Binomial(n=24, p=0.5): P(X = 21) = ___ 5. E[X] for X with values {20, 22, 24} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.48 ___

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Patterns and rules

1. P(A) = 1.8, P(B) = 1.9. If independent, P(A∩B) = ___ 2. Binomial(n=35, p=0.5): P(X = 32) = ___ 3. E[X] for X with values {31, 33, 35} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree